Sky routers should just be plug and play... mine was (though I did have a few problems with wireless at first)
I'd start by hitting the factory reset button on the back of the router and then connecting to it using a wired connection with sky's instructions in front of you.
Turn off all firewalls on the PC... I have seen problems before when both the Windows Firewall and another (Norton, McAfee...) have been active simultaneously.
Download some of the anti-malware scanners onto a memory stick and try running those to see if there's anything nasty lurking. (A-squared do a version that can be run from the USB stick) also MBAM is good
Try booting into Safe-Mode with networking and see if you can connect out in this mode.

